Thank you Martin for the help.I did different test by using 2p model with box
and centered Finite volume and I found what you have mentioned.Can I also use
higher order time method in Dumux?
Thank youHai
On Monday, November 24, 2014 9:54 PM, Martin
<[email protected]> wrote:
Hello Hai,
as far as I know you usually look at strong convergence rates (every strongly
convergent sequence is also weakly convergent). That means |u-u_h| -> 0 (in the
corresponding Hilbert norm) implies strong convergence. As Christoph already
mentioned, for the box method you get in general first order accuracy: second
order for pressure which implies first order for velocity and first order in
time because of backward or forward Euler method.
For the cell centered Finite Volume Scheme with Two-Point Flux Approximation
you only achieve this rates for isotropic permeability tensors. If you want to
achieve first order for general grids and permeability tensors you can use
Multi-Point-Flux approximations.
Regards,
Martin
On 11/24/2014 05:42 PM, Christoph Grüninger wrote:
Hello Hai,
what do you mean by weak and strong convergence rate?
A student of my checked the L2 error for refined grids and time steps
with the Richards equation and the FV method. We got the expected first
order convergence.
You can find the detail in his Bachelor's thesis, but it is German
"Baccour, M.H.: Verifikationsproblem mit bekannter Lösung für die
Zwei-Phasen-Darcy-Gleichung"
Additional there was a Master's thesis by Markus Wolff, it's written in
English and might help. I haven't checked myself, Bernd told me that:
"Wolff, M.: Comparison of mathematical and numerical models for twophase
flow in porous media."
Just out of curiosity: What's your affiliation?
Bye,
Christoph
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